A trick to compute certain Manin products of operads

TL;DR

This paper introduces straightforward techniques for computing Manin black products involving key operads like associative, commutative, and pre-Lie, simplifying complex algebraic calculations.

Contribution

It provides novel, simple methods to compute Manin black products with fundamental operads, aiding algebraic research and computations.

Findings

Simplified computation methods for Manin black products.

Applicable to operads like $ ext{Ass}$, $ ext{Com}$, and $ ext{pre} ext{Lie}$.

Facilitates algebraic structure analysis.

Abstract

We describe simple tricks to compute the Manin black products with the operads $\mathcal{A}ss$, $\mathcal{C}om$ and $pre\mathcal{L}ie$.